Bayesian Model Selection in Complex Linear Systems, as Illustrated in Genetic Association Studies

Motivated by examples from genetic association studies, this paper considers the model selection problem in a general complex linear model system and in a Bayesian framework. We discuss formulating model selection problems and incorporating context-dependent {\it a priori} information through different levels of prior specifications. We also derive analytic Bayes factors and their approximations to facilitate model selection and discuss their theoretical and computational properties. We demonstrate our Bayesian approach based on an implemented Markov Chain Monte Carlo (MCMC) algorithm in simulations and a real data application of mapping tissue-specific eQTLs. Our novel results on Bayes factors provide a general framework to perform efficient model comparisons in complex linear model systems

Statistical and Computational Methods for Genome-Wide Association Analysis

Technological and scientific advances in recent years have revolutionized genomics. For example, decreases in whole genome sequencing (WGS) costs have enabled larger WGS studies as well as larger imputation reference panels, which in turn provide more comprehensive genomic coverage from lower-cost genotyping methods. In addition, new technologies and large collaborative efforts such as ENCODE and GTEx have shed new light on regulatory genomics and the function of non-coding variation, and produced expansive publicly available data sets. These advances have introduced data of unprecedented size and dimension, unique statistical and computational challenges, and numerous opportunities for innovation. In this dissertation, we develop methods to leverage functional genomics data in post-GWAS analysis, to expedite routine computations with increasingly large genetic data sets, and to address limitations of current imputation reference panels for understudied populations. In Chapter 2, we propose strategies to improve imputation and increase power in GWAS of understudied populations. Genotype imputation is instrumental in GWAS, providing increased genomic coverage from low-cost genotyping arrays. Imputation quality depends crucially on reference panel size and the genetic distance between reference and target haplotypes. Current reference panels provide excellent imputation quality in many European populations, but lower quality in non-European, admixed, and isolate populations. We consider a GWAS strategy in which a subset of participants is sequenced and the rest are imputed using a reference panel that comprises the sequenced participants together with individuals from an external reference panel. Using empirical data from the HRC and TOPMed WGS Project, simulations, and asymptotic analysis, we identify powerful and cost-effective study designs for GWAS of non-European, admixed, and isolated populations. In Chapter 3, we develop efficient methods to estimate linkage disequilibrium (LD) with large data sets. Motivated by practical and logistical constraints, a variety of statistical methods and tools have been developed for analysis of GWAS summary statistics rather than individual-level data. These methods often rely on LD estimates from an external reference panel, which are ideally calculated on-the-fly rather than precomputed and stored. We develop efficient algorithms to estimate LD exploiting sparsity and haplotype structure and implement our methods in an open-source C++ tool, emeraLD. We benchmark performance using genotype data from the 1KGP, HRC, and UK Biobank, and find that emeraLD is up to two orders of magnitude faster than existing tools while using comparable or less memory. In Chapter 4, we develop methods to identify causative genes and biological mechanisms underlying associations in post-GWAS analysis by leveraging regulatory and functional genomics databases. Many gene-based association tests can be viewed as instrumental variable methods in which intermediate phenotypes, e.g. tissue-specific expression or protein alteration, are hypothesized to mediate the association between genotype and GWAS trait. However, LD and pleiotropy can confound these statistics, which complicates their mechanistic interpretation. We develop a hierarchical Bayesian model that accounts for multiple potential mechanisms underlying associations using functional genomic annotations derived from GTEx, Roadmap/ENCODE, and other sources. We apply our method to analyze twenty-five complex traits using GWAS summary statistics from UK Biobank, and provide an open-source implementation of our methods. In Chapter 5, we review our work, discuss its relevance and prospects as new resources emerge, and suggest directions for future research.PHDBiostatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/147697/1/corbinq_1.pd

OPENMENDEL: A Cooperative Programming Project for Statistical Genetics

Statistical methods for genomewide association studies (GWAS) continue to improve. However, the increasing volume and variety of genetic and genomic data make computational speed and ease of data manipulation mandatory in future software. In our view, a collaborative effort of statistical geneticists is required to develop open source software targeted to genetic epidemiology. Our attempt to meet this need is called the OPENMENDELproject (https://openmendel.github.io). It aims to (1) enable interactive and reproducible analyses with informative intermediate results, (2) scale to big data analytics, (3) embrace parallel and distributed computing, (4) adapt to rapid hardware evolution, (5) allow cloud computing, (6) allow integration of varied genetic data types, and (7) foster easy communication between clinicians, geneticists, statisticians, and computer scientists. This article reviews and makes recommendations to the genetic epidemiology community in the context of the OPENMENDEL project.Comment: 16 pages, 2 figures, 2 table

Dynamic incorporation of multiple in silico functional annotations empowers rare variant association analysis of large whole-genome sequencing studies at scale

Large-scale whole-genome sequencing studies have enabled the analysis of rare variants (RVs) associated with complex phenotypes. Commonly used RV association tests have limited scope to leverage variant functions. We propose STAAR (variant-set test for association using annotation information), a scalable and powerful RV association test method that effectively incorporates both variant categories and multiple complementary annotations using a dynamic weighting scheme. For the latter, we introduce \u27annotation principal components\u27, multidimensional summaries of in silico variant annotations. STAAR accounts for population structure and relatedness and is scalable for analyzing very large cohort and biobank whole-genome sequencing studies of continuous and dichotomous traits. We applied STAAR to identify RVs associated with four lipid traits in 12,316 discovery and 17,822 replication samples from the Trans-Omics for Precision Medicine Program. We discovered and replicated new RV associations, including disruptive missense RVs of NPC1L1 and an intergenic region near APOC1P1 associated with low-density lipoprotein cholesterol

Increasing power for voxel-wise genome-wide association studies : the random field theory, least square kernel machines and fast permutation procedures

Imaging traits are thought to have more direct links to genetic variation than diagnostic measures based on cognitive or clinical assessments and provide a powerful substrate to examine the influence of genetics on human brains. Although imaging genetics has attracted growing attention and interest, most brain-wide genome-wide association studies focus on voxel-wise single-locus approaches, without taking advantage of the spatial information in images or combining the effect of multiple genetic variants. In this paper we present a fast implementation of voxel- and cluster-wise inferences based on the random field theory to fully use the spatial information in images. The approach is combined with a multi-locus model based on least square kernel machines to associate the joint effect of several single nucleotide polymorphisms (SNP) with imaging traits. A fast permutation procedure is also proposed which significantly reduces the number of permutations needed relative to the standard empirical method and provides accurate small p-value estimates based on parametric tail approximation. We explored the relation between 448,294 single nucleotide polymorphisms and 18,043 genes in 31,662 voxels of the entire brain across 740 elderly subjects from the Alzheimer's Disease Neuroimaging Initiative (ADNI). Structural MRI scans were analyzed using tensor-based morphometry (TBM) to compute 3D maps of regional brain volume differences compared to an average template image based on healthy elderly subjects. We find method to be more sensitive compared with voxel-wise single-locus approaches. A number of genes were identified as having significant associations with volumetric changes. The most associated gene was GRIN2B, which encodes the N-methyl-d-aspartate (NMDA) glutamate receptor NR2B subunit and affects both the parietal and temporal lobes in human brains. Its role in Alzheimer's disease has been widely acknowledged and studied, suggesting the validity of the approach. The various advantages over existing approaches indicate a great potential offered by this novel framework to detect genetic influences on human brains

Statistical methods for gene selection and genetic association studies

This dissertation includes five Chapters. A brief description of each chapter is organized as follows. In Chapter One, we propose a signed bipartite genotype and phenotype network (GPN) by linking phenotypes and genotypes based on the statistical associations. It provides a new insight to investigate the genetic architecture among multiple correlated phenotypes and explore where phenotypes might be related at a higher level of cellular and organismal organization. We show that multiple phenotypes association studies by considering the proposed network are improved by incorporating the genetic information into the phenotype clustering. In Chapter Two, we first illustrate the proposed GPN to GWAS summary statistics. Then, we assess contributions to constructing a well-defined GPN with a clear representation of genetic associations by comparing the network properties with a random network, including connectivity, centrality, and community structure. The network topology annotations based on the sparse representations of GPN can be used to understand the disease heritability for the highly correlated phenotypes. In applications of phenome-wide association studies, the proposed GPN can identify more significant pairs of genetic variant and phenotype categories. In Chapter Three, a powerful and computationally efficient gene-based association test is proposed, aggregating information from different gene-based association tests and also incorporating expression quantitative trait locus information. We show that the proposed method controls the type I error rates very well and has higher power in the simulation studies and can identify more significant genes in the real data analyses. In Chapter Four, we develop six statistical selection methods based on the penalized regression for inferring target genes of a transcription factor (TF). In this study, the proposed selection methods combine statistics, machine learning , and convex optimization approach, which have great efficacy in identifying the true target genes. The methods will fill the gap of lacking the appropriate methods for predicting target genes of a TF, and are instrumental for validating experimental results yielding from ChIP-seq and DAP-seq, and conversely, selection and annotation of TFs based on their target genes. In Chapter Five, we propose a gene selection approach by capturing gene-level signals in network-based regression into case-control association studies with DNA sequence data or DNA methylation data, inspired by the popular gene-based association tests using a weighted combination of genetic variants to capture the combined effect of individual genetic variants within a gene. We show that the proposed gene selection approach have higher true positive rates than using traditional dimension reduction techniques in the simulation studies and select potentially rheumatoid arthritis related genes that are missed by existing methods